The present invention relates to a method and a system for assisting the piloting of an aircraft during an operational flight phase in the course of which the aircraft is likely to land on a runway. Such an operational flight phase can notably correspond to an approach phase for the purpose of a landing on the runway. In order to land an aircraft, in particular a transport aircraft, on a runway, that aircraft flying at a current moment of time with a current energy, it is necessary to manage the dissipation of its energy during the approach to the runway in such a way that on the one hand the contact of the aircraft with the ground is not too abrupt and, on the other hand, once the aircraft is on the ground, it has sufficient braking capability to stop before an end of the runway. In order to do this, the landing procedures make provision for the aircraft to be in a state called a “stabilized state” when during its descent it reaches a predetermined height with respect to the ground, defined in the landing procedure chosen by the pilot. The predetermined height can for example be 1000 feet (about 300 meters) or 500 feet (about 150 meters). The stabilized state corresponds to stabilized approach conditions, which notably comprise a predetermined and stabilized approach speed and approach slope (that is to say they are constant over the course of time) defined in the landing procedure in question. These stabilized approach conditions must be maintained during the continuation of the approach to the runway, down to a height of for example 50 feet (about 15 meters) in direct proximity to the runway. The energy of the aircraft at a given time corresponds to the sum, on the one hand, of its potential energy because of the difference in height between the position of the aircraft at that time and the position of the runway and, on the other hand, of its kinetic energy at that time.
When a pilot of the aircraft wishes to fly such an operational phase during the course of which the aircraft is likely to land on a runway, it is desirable that he should have indicators in the cockpit of the aircraft allowing him to appreciate if it is possible to land the aircraft on that runway in good conditions. In particular, it is desirable that these indicators allow the pilot to appreciate if it is possible to manage a dissipation of the current energy of the aircraft during its approach to the runway making it possible to reach a stabilized state at said predetermined height, in order that, on the one hand, the contact with the ground is not too abrupt and, on the other hand, once the aircraft is on the ground, it has sufficient braking capability to stop before an end of the runway. The documents FR2885439 and FR2908220 describe the display of a first arc of a circle and of a second arc of a circle on a navigation screen in the cockpit, these two arcs of a circle, the first one corresponding to a minimum approach distance conforming with an optimized approach for reaching stabilized approach conditions and the second one corresponding to a standard approach distance conforming with a standard approach for reaching stabilized approach conditions, each of said distances being defined between projections in a horizontal plane of a current position of the aircraft and a position of contact of the aircraft with the ground. Said minimum approach distance conforming to an optimized approach corresponds to a strategy of maximum dissipation of the energy of the aircraft, and therefore to a maximum deceleration of the aircraft in consideration of its operational performance, in particular by applying optimized management of the aerodynamic configuration (air brakes . . . ) of the aircraft. The two arcs of a circle allow the pilot to better comprehend the capability of the aircraft to land on the runway in good conditions, by comparing the positions of said arcs of a circle with a position of the runway shown on the navigation screen. However, the display of said arcs of a circle on the navigation screen depends on the display extent (range) selected by the pilot for display on the navigation screen. If the display range selected by the pilot is not sufficient, these arcs of a circle cannot be displayed on the screen and the pilot is not therefore informed of the capability of the aircraft to land on the runway in good conditions. On the other hand, when the navigation screen is configured in ARC mode and the runway is situated behind the aircraft, the position of the runway is not displayed on the navigation screen. Even if the two arcs of a circle are displayed, they do not allow the pilot to appreciate the capability of the aircraft to land on the runway in good conditions since the latter is not shown on the screen. Such a situation is shown in FIG. 1. This figure shows a navigation screen of the ND (Navigation Display) type on which the following are displayed in the usual manner:                a symbol 10 representing the current position of the aircraft;        a usual distance scale 17, defined with respect to the current position of the aircraft illustrated by the symbol 10;        a usual scale 16 of angular deviations;        a plot 13 illustrating the theoretical fight path of the aircraft in projection in the horizontal plane, with waypoints 15.        
On this screen are also shown, in front of the aircraft, the first arc of a circle C1 associated with the minimum approach distance and the second arc of a circle C2 associated with the standard approach distance. In the example shown in the figure, the runway is situated behind the aircraft and consequently it is not visible on the navigation screen. It is therefore difficult for the pilot to interpret the display of the two arcs of a circle C1 and C2.